Answer:
Step-by-step explanation:
18 is the height of it and then you divide 690
Answer:

Step-by-step explanation:






<u>Answer:</u>
A) 720 ways
B) 15 ways
C) 6 ways
<u>Step-by-step explanation:</u>
A) To find the number of ways Alicia can arranger her 6 paintings, we will find factorial of 6 by multiplying all of the positive integers equal to or less than that number i.e. 6 to get:
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
Alicia can arrange her paintings in 720 ways.
B) We use the following formula (when order is not important) to find the number of permutations of n objects taken r at a time:


Therefore, Alicia can choose any 4 of her paintings in 15 ways.
C) Number of ways Alicia can arrange 3 out of 6 paintings = 3! = 3*2*1 = 6 ways
Let
h: height of the water
r: radius of the circular top of the water
V: the volume of water in the cup.
We have:
r/h = 3/10
So,
r = (3/10)*h
the volume of a cone is:
V = (1/3)*π*r^2*h
Rewriting:
V (t) = (1/3)*π*((3/10)*h(t))^2*h(t)
V (t) =(3π/100)*h(t)^3
Using implicit differentiation:
V'(t) = (9π/100)*h(t)^2*h'(t)
Clearing h'(t)
h'(t)=V'(t)/((9π/100)*h(t)^2)
the rate of change of volume is V'(t) = 2 cm3/s when h(t) = 5 cm.
substituting:
h'(t) = 8/(9π) cm/s
Answer:
the water level is rising at a rate of:
h'(t) = 8/(9π) cm/s